Abstract

Fundamental difficulties arise in the attempt to measure the optical transfer function at high spatial frequencies. These difficulties are due to the basic nonlinearity of optical imaging systems at high spatial frequencies. The physical significance of this nonlinearity in image evaluation is illustrated by considering two commonly used methods of measuring the optical transfer function, i.e., the imaging of sine waves and edges. It is shown that at spatial frequencies considered to be within the state of the art, both of these methods lead to apparent, or measured, transfer functions which are significantly different from those which would be obtained for a linear system. For the practical case where the object mutual intensity is spatially stationary, it is found that the importance of this nonlinearity is determined by the ratio of the coherence interval of the object illumination to the size of the imaging system's diffraction pattern. These nonlinearities can therefore become important at lower spatial frequencies. The implications of these results for image evaluation are discussed.

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  1. R. C. Bourret, Nuovo Cimento 18, 347 (1960).
  2. J. Sarfatt, Nuovo Cimento 27, 1119 (1963).
  3. M. Beran and G. Parrent, Jr., Nuovo Cimento 27, 1049 (1963).
  4. H. H. Hopkins, J. Opt. Soc. Am. 47, 508 (1957).
  5. W. H. Steel, J. Opt. Soc. Am. 47, 405 (1957).
  6. D. Canals-Frau and M. Rousseau, Opt. Acta 5, 15 (1958).
  7. A. Maréchal and M. Francon, Diffraction, Structure des Images, (Editions Revue d'Optique, Paris, 1960).
  8. M. De and S. C. Som, J. Opt. Soc. Am. 53, 779 (1963).
  9. W. N. Charman, J. Opt. Soc. Am. 53, 410 (1963).
  10. W. T. Welford, Optics in Metrology (Pergamon Press, New York, 1960), p. 85.
  11. R. E. Kinzly, J. Opt. Soc. Am. 55, 1002 (1965).
  12. M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1964), Ch. 10.
  13. M. Beran and G. Parrent, Jr., Theory of Partial Coherence (Prentice Hall, Englewood Cliffs, N. J., 1964).
  14. L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
  15. Reference 12, p. 508. In the general statement of the van Cittert-Zernike theorem, a quadratic phase factor appears in front of the integral in (13). For the large sources with which we are concerned, this phase factor is approximately unity over the region where Γ012) is nonzero.

Beran, M.

M. Beran and G. Parrent, Jr., Nuovo Cimento 27, 1049 (1963).

M. Beran and G. Parrent, Jr., Theory of Partial Coherence (Prentice Hall, Englewood Cliffs, N. J., 1964).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1964), Ch. 10.

Bourret, R. C.

R. C. Bourret, Nuovo Cimento 18, 347 (1960).

Canals-Frau, D.

D. Canals-Frau and M. Rousseau, Opt. Acta 5, 15 (1958).

Charman, W. N.

W. N. Charman, J. Opt. Soc. Am. 53, 410 (1963).

De, M.

M. De and S. C. Som, J. Opt. Soc. Am. 53, 779 (1963).

Francon, M.

A. Maréchal and M. Francon, Diffraction, Structure des Images, (Editions Revue d'Optique, Paris, 1960).

Hopkins, H. H.

H. H. Hopkins, J. Opt. Soc. Am. 47, 508 (1957).

Kinzly, R. E.

R. E. Kinzly, J. Opt. Soc. Am. 55, 1002 (1965).

Mandel, L.

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).

Maréchal, A.

A. Maréchal and M. Francon, Diffraction, Structure des Images, (Editions Revue d'Optique, Paris, 1960).

Parrent, Jr., G.

M. Beran and G. Parrent, Jr., Nuovo Cimento 27, 1049 (1963).

M. Beran and G. Parrent, Jr., Theory of Partial Coherence (Prentice Hall, Englewood Cliffs, N. J., 1964).

Rousseau, M.

D. Canals-Frau and M. Rousseau, Opt. Acta 5, 15 (1958).

Sarfatt, J.

J. Sarfatt, Nuovo Cimento 27, 1119 (1963).

Som, S. C.

M. De and S. C. Som, J. Opt. Soc. Am. 53, 779 (1963).

Steel, W. H.

W. H. Steel, J. Opt. Soc. Am. 47, 405 (1957).

Welford, W. T.

W. T. Welford, Optics in Metrology (Pergamon Press, New York, 1960), p. 85.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1964), Ch. 10.

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).

Other (15)

R. C. Bourret, Nuovo Cimento 18, 347 (1960).

J. Sarfatt, Nuovo Cimento 27, 1119 (1963).

M. Beran and G. Parrent, Jr., Nuovo Cimento 27, 1049 (1963).

H. H. Hopkins, J. Opt. Soc. Am. 47, 508 (1957).

W. H. Steel, J. Opt. Soc. Am. 47, 405 (1957).

D. Canals-Frau and M. Rousseau, Opt. Acta 5, 15 (1958).

A. Maréchal and M. Francon, Diffraction, Structure des Images, (Editions Revue d'Optique, Paris, 1960).

M. De and S. C. Som, J. Opt. Soc. Am. 53, 779 (1963).

W. N. Charman, J. Opt. Soc. Am. 53, 410 (1963).

W. T. Welford, Optics in Metrology (Pergamon Press, New York, 1960), p. 85.

R. E. Kinzly, J. Opt. Soc. Am. 55, 1002 (1965).

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1964), Ch. 10.

M. Beran and G. Parrent, Jr., Theory of Partial Coherence (Prentice Hall, Englewood Cliffs, N. J., 1964).

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).

Reference 12, p. 508. In the general statement of the van Cittert-Zernike theorem, a quadratic phase factor appears in front of the integral in (13). For the large sources with which we are concerned, this phase factor is approximately unity over the region where Γ012) is nonzero.

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